Various processes for the preparation of monocrystals are currently known, which processes may be exploited on an industrial scale.
An especially interesting such process consists in growing the monocrystal from a melt bath of the compound to be crystallised, in particular by implementing the conventional method known as the Czochralski method. Such a method offers, inter alia, the advantage of leading to especially fast rates of crystal growth, typically of the order of several centimeters per day.
However, growing crystals from melt baths is not possible for some compounds, notably those exhibiting non-congruent melting (i.e. those which have a composition in the liquid state which differs from that in the solid state due, for example, to chemical decomposition phenomena or peritectics), and for those having a transition phase between the molten and the liquid state within a temperature zone between their melting temperature and the ambient temperature. Thus, the melt bath process is shown in fact to be unsuitable for the crystallisation of numerous compounds such as, among numerous other examples, the α-form of quartz (α-SiO2), some phosphates (such as KH2PO4, KTiOPO4, for example), some borates (such as YAl3(BO3)4), and even certain metal halides.
For the crystallisation of compounds unsuited to the melt bath process, such as those mentioned above, it has been proposed to implement methods of growing crystals in solution, wherein the compound to be crystallised is initially dissolved in a solvent, and growth is produced by exposing the solution to super-saturation conditions, that is, conditions wherein the solute is at a concentration greater than its solubility.
In methods of this type, at any given instant the supersaturation state of the solution in which crystallisation has occurred may be quantified by its relative supersaturation, represented by s and calculated according to the following relationship:
  s  =            (              C        -                  C          0                    )              C      0      wherein:                C represents the concentration of dissolved compound in the solution; and        C0 represents the solubility of the dissolved compound at the temperature at which crystallisation occurs.        
This state of supersaturation, a prerequisite for crystallisation in solution, is conventionally obtained using two kinds of methods:                by solvent evaporation:        according to this first variant, the quantity of solvent in the solution is reduced in the course of crystallisation, generally by allowing the said solvent to evaporate gradually, leading to an increase in the compound/solvent ratio in the medium, which enables the concentration to be initially increased to achieve the supersaturation required to initiate crystallisation, and then allows the supersaturated state to be maintained in proportion as the compound in solution is consumed to form the crystal.        by temperature change:        according to this alternative variant, the temperature of the solution is altered in such a way as to induce a decrease in the solubility of the compound to be crystallised in the crystallisation solution, so as to obtain the desired supersaturation. For the majority of compounds, solubility increases with temperature; the desired decrease in solubility is therefore usually obtained by reducing the temperature of the crystallisation solution. Nevertheless, there are a number of individual compounds, limestone for example, the solubility of which is retrograde, i.e. it decreases as temperature rises. For this type of compound, the converse happens, the desired decrease in solubility is achieved by raising the temperature.        In the methods which employ a change in temperature, supplementary control of the reaction conditions proves necessary in order to sustain the crystallisation process. This is because the crystal formation produced by the temperature change consumes the compound in solution, lowering the concentration of the said compound in the crystallisation solution, the very thing which induces a tendency to deviate from the required supersaturation conditions. To counterbalance this phenomenon of desaturation of the solution and maintain a state of supersaturation, a specific possibility consists in carrying out a continuous temperature modification (usually a continuous lowering of the temperature or, more specifically, a continuous increase in the specific case of compounds of retrograde solubility).        
The aforementioned methods of crystallisation, by evaporation of solvent or temperature change, usually prove unsuitable for implementation on an industrial scale for the preparation of crystals of large dimension.
In this regard it should first of all be noted that the currently known methods of crystallogenesis in solution do not permit control of the thermodynamic and kinetic conditions of crystal formation:                in the case of crystal growth by solvent evaporation, the conditions of crystallisation (volume of the reaction medium, concentration) change constantly as the reaction progresses. In particular the concentration of impurities in solution tends to increase in the course of crystal growth, leading to an increase over time in the incorporation of these impurities in the forming crystals. Furthermore, the process of evaporation is itself often difficult to control. Methods of crystal growth by solvent evaporation are therefore in practice used only in the laboratory and actually have found no use on an industrial scale.        similarly, in methods employing a temperature change, this change in temperature again causes a change in the thermodynamic and kinetic conditions during crystallogenesis, and maintaining supersaturation throughout the growth phase is difficult to achieve and in fact remains empirical.        
The changing conditions of crystallogenesis produced within the framework of current methods of crystal growth in solution has a direct impact on the quality of the crystals produced.
These changing conditions of crystal growth prove especially problematic when it is intended to grow crystals which are not based on definite compounds, but on intermediate compositions such as, for example, solid solutions or doped compounds (especially intermediate compositions of substituted solid solutions wherein a plurality of atom types of differing chemical nature occupy the same site on the crystalline structure, and/or compounds doped with interstitial members, for example crystals doped with insertion ions).
Indeed, in this circumstance the change in the thermodynamic and kinetic conditions is usually associated with substantial modifications in the mechanisms of crystal formation. These modifications may especially lead to a variation in the rate of incorporation of substituent and/or interstitial species and therefore give rise to inhomogeneities in the composition of the crystal formed. These instabilities may similarly lead to the formation of defects in the crystalline structure (defects in the lattice arrangement, dislocations, etc.), and in extreme cases to the insertion of solvent into the crystal. More generally, these different phenomena are capable of leading to a degradation in the quality of the crystal. Typically, the gradual change in the rate of incorporation of substituent and/or doping members and/or of impurities may especially induce a progressive change in the crystalline mesh parameters during growth, usually leading to tensions within the crystal, a cause of numerous crystalline defects such as dislocations, or even more macroscopic fractures. The larger the size of the crystal formed, the more substantial are these phenomena.
Another more general problem encountered with the use of currently known methods of crystal growth in solution is that these methods generally yield limited rates of crystal growth distinctly slower than those obtained with processes using melt baths.
Indeed, in methods of crystallogenesis in solution, the rate of crystal growth is directly proportional to the relative supersaturation of the solution in which the crystallisation is carried out.
In the majority of cases, notably to avoid spontaneous nucleation of crystallites, conventional crystal growth in solution is typically carried out at low rates of supersaturation s, typically of around 1-5%, corresponding to rates of crystal growth in solution of the order of a few millimeters per day. With this type of reduced crystal growth rate, the preparation of monocrystals several centimeters in dimension may take a number of weeks or even months. For some compounds, the preparation time is even of the order of one year or longer.
To try to counter this difficulty, a method of crystal growth by temperature reduction has been developed wherein it is proposed to filter and heat-treat the solution so as to avoid spontaneous nucleation, which makes it possible to increase the rate of temperature reduction with the aim of increasing the supersaturation and thus the rate of crystal growth. Within this framework, methods of preparing giant crystals of potassium disphosphate KH2PO4 (or KDP) have been described, wherein one has attempted to increase the supersaturation state to values of the order of 30% with the aim of increasing growth rates to 3-4 cm/day. While such methods prove effective with crystals of relatively small size (of the order of a few centimeters), the growth rate remains limited in practice when forming crystals of larger dimension (for example of the order of about 10 centimeters or more). Moreover, the rates of temperature reduction necessary to obtain significant rates of crystal growth produce a thermal gradient between the centre of the forming macrocrystals and the periphery of the crystal in contact with the colder solution. This gradient creates stresses within the crystal which usually induce fracture phenomena when excessively high rates of growth are employed. Thus, although supersaturation of 30% and growth rates of 3 cm/day have been achieved, the growth of monocrystals of large size using this system based on temperature reduction is only possible at rates of at most 1 cm/day.